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Simplifying (2a + -3)(a + 7) = 0 Reorder the terms: (-3 + 2a)(a + 7) = 0 Reorder the terms: (-3 + 2a)(7 + a) = 0 Multiply (-3 + 2a) * (7 + a) (-3(7 + a) + 2a * (7 + a)) = 0 ((7 * -3 + a * -3) + 2a * (7 + a)) = 0 ((-21 + -3a) + 2a * (7 + a)) = 0 (-21 + -3a + (7 * 2a + a * 2a)) = 0 (-21 + -3a + (14a + 2a2)) = 0 Combine like terms: -3a + 14a = 11a (-21 + 11a + 2a2) = 0 Solving -21 + 11a + 2a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + -1a)(3 + -2a) = 0Subproblem 1
Set the factor '(-7 + -1a)' equal to zero and attempt to solve: Simplifying -7 + -1a = 0 Solving -7 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1a = 0 + 7 -1a = 0 + 7 Combine like terms: 0 + 7 = 7 -1a = 7 Divide each side by '-1'. a = -7 Simplifying a = -7Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {-7, 1.5}
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